Geometrically non-linear multi-layer beam with interconnection allowing for mixed-mode delamination

Škec, Leo; Jelenić, Gordan

doi:10.1016/j.engfracmech.2016.11.003

Cited by 8 publications

(9 citation statements)

References 19 publications

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“…Instead of giving a general mathematical formulation of a stack of alternating beam and interface elements, effectively producing a macro‐element with a number of degrees of freedom (DOFs) dependent on the number of layers, 24 Russo and Chen 20 implemented an independent interface element that can be connected to Euler–Bernoulli (EB) beam finite elements. They confirmed and additionally elaborated the benefits of modeling delamination using beam finite elements previously reported in References 15 and 24.…”

Section: Introductionsupporting

confidence: 78%

“…Although in this figure, a small gap is depicted between the layers, in the present work it will be assumed that the interface between components has zero thickness, which is a common approach. 16 Moreover, it can be easily shown 15 that for this type of interface elements, the relative displacements at the interface, and therefore the stresses transmitted between the components, are independent of the thickness of the interface. In this work, we will denote as BINT4 the interface element that can be used in conjunction with two-node beam finite elements, where "B" stands for "beam," "INT" for "interface" and "4" is the element's number of nodes.…”

Section: Fe Implementation Of the Beam-linked Interface Elementmentioning

confidence: 99%

“…In many situations (such as standard delamination tests 6‐8 ), however, out‐of‐plane effects can be neglected and, for the sake of reducing the computational burden, such simulations are usually performed using 2D models, where the third mode of delamination (scissoring shear) is excluded. Regardless of whether the analysis is 2D or 3D, the interface elements with embedded CMZs introduce material nonlinearity in the numerical model of the type that often causes convergence problems and requires more advanced and robust solution algorithms 13‐15 . In front of the crack tip, the resulting distribution of interface tractions is highly nonlinear and can include a transition from tensile to compressive tractions over a very small distance.…”

Section: Introductionmentioning

confidence: 99%

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Mixed‐mode delamination of layered structures modeled as Timoshenko beams with linked interpolation

Ranjbar

Škec

Jelenić

et al. 2022

Numerical Meth Engineering

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In this work, a finite-element formulation for modeling mixed-mode delamination in layered structures, consisting of two-node Timoshenko beam finite elements with quadratic linked interpolation and corresponding 4-node interface elements is presented and compared to a more common approach where linear Lagrange interpolation is used. The principal novelty of the proposed approach is that the vertical displacements of the beam elements, as well as the transversal relative displacements of the interface elements, are interpolated using a quadratic linked interpolation that also takes into account the nodal cross-sectional rotations of the beam elements. At the same time, the axial displacements and cross-sectional rotations are interpolated using linear Lagrange polynomials. A bilinear cohesive zone model is embedded in the interface finite elements for delamination modes I and II. Numerical analyses based on the examples from the literature with metal joints show that the formulation with quadratic linked interpolation improves the convergence and robustness of the solution with respect to the approach with linear interpolation. On the other hand, in case of composites with stiff adhesives this formulation exhibits a peculiar behavior with spurious oscillations of the normal interface tractions that leads to a poor performance in mode-I and mixed-mode tests. This problem can be easily solved by canceling the quadratic term in the interpolation function and using the standard Lagrange interpolation in such cases.

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Section: Introductionsupporting

confidence: 78%

Section: Fe Implementation Of the Beam-linked Interface Elementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mixed‐mode delamination of layered structures modeled as Timoshenko beams with linked interpolation

Ranjbar

Škec

Jelenić

et al. 2022

Numerical Meth Engineering

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“…The results were presented for single-mode (I and II) and mixed-mode delamination problems in geometrically linear (Škec et al. 2015 ) and non-linear analysis (Škec and Jelenić 2017 ). Compared to models which use plane solid FEs, the computational efficiency of the beam model was improved (the reduction of total number of degrees of freedom can go up to 40 %) without any significant loss in the accuracy.…”

Section: Introductionmentioning

confidence: 99%

Complete analytical solutions for double cantilever beam specimens with bi-linear quasi-brittle and brittle interfaces

2018

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In this work we develop a complete analytical solution for a double cantilever beam (DCB) where the arms are modelled as Timoshenko beams, and a bi-linear cohesive-zone model (CZM) is embedded at the interface. The solution is given for two types of DCB; one with prescribed rotations (with steady-state crack propagation) and one with prescribed displacement (where the crack propagation is not steady state). Because the CZM is bi-linear, the analytical solutions are given separately in three phases, namely (i) linear-elastic behaviour before crack propagation, (ii) damage growth before crack propagation and (iii) crack propagation. These solutions are then used to derive the solutions for the case when the interface is linear-elastic with brittle failure (i.e. no damage growth before crack propagation) and the case with infinitely stiff interface with brittle failure (corresponding to linear-elastic fracture mechanics (LEFM) solutions). If the DCB arms are shear-deformable, our solution correctly captures the fact that they will rotate at the crack tip and in front of it even if the interface is infinitely stiff. Expressions defining the distribution of contact tractions at the interface, as well as shear forces, bending moments and cross-sectional rotations of the arms, at and in front of the crack tip, are derived for a linear-elastic interface with brittle failure and in the LEFM limit. For a DCB with prescribed displacement in the LEFM limit we also derive a closed-form expression for the critical energy release rate, . This formula, compared to the so-called ‘standard beam theory’ formula based on the assumptions that the DCB arms are clamped at the crack tip (and also used in standards for determining fracture toughness in mode-I delamination), has an additional term which takes into account the rotation at the crack tip. Additionally, we provide all the mentioned analytical solutions for the case when the shear stiffness of the arms is infinitely high, which corresponds to Euler–Bernoulli beam theory. In the numerical examples we compare results for Euler–Beronulli and Timoshenko beam theory and analyse the influence of the CZM parameters.

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“…Reinoso et al [51] developed a nonlinear finite thickness cohesive element based on solid shell concept for delamination in composite laminates. Comparisons between linear and nonlinear formulations were discussed and the necessity of incorporation of geometrically nonlinear effects was verified in a recent work byŠkec and Jelenić [52]. However, these methods are not readily applicable to a general problem with both matrix cracking and delamination process [38,45].…”

mentioning

confidence: 99%

Geometrically nonlinear analysis of matrix cracking and delamination in composites with floating node method

2018

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Geometrically non-linear multi-layer beam with interconnection allowing for mixed-mode delamination

Cited by 8 publications

References 19 publications

Mixed‐mode delamination of layered structures modeled as Timoshenko beams with linked interpolation

Mixed‐mode delamination of layered structures modeled as Timoshenko beams with linked interpolation

Complete analytical solutions for double cantilever beam specimens with bi-linear quasi-brittle and brittle interfaces

Geometrically nonlinear analysis of matrix cracking and delamination in composites with floating node method

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